from collections import defaultdict, deque

# 1) the forward edge graph
forward = {
    2:  [3, 8],
    3:  [4],
    4:  [5, 8, 14],
    5:  [6],
    6:  [14],
    7:  [],
    8:  [9],
    9:  [10],
    10: [12],
    11: [14],
    12: [11],
    13: [],
    14: []
}

# prereqs[v] = list of u
prereqs = defaultdict(list)
for u, vs in forward.items():
    for v in vs:
        prereqs[v].append(u)

# 2) Part 1: perform BFS with flipped graph from 14 to collect ancestors
rev = defaultdict(list)
for u, vs in forward.items():
    for v in vs:
        rev[v].append(u)

ancestors = set()
q = deque([14])
while q:
    v = q.popleft()
    if v in ancestors:
        continue
    ancestors.add(v)
    for u in rev[v]:
        q.append(u)

# 3) Part 2: loop to get prereqs from ancestors
schedule   = []
covered    = set()
remaining  = set(ancestors)

while remaining:
    # find any chapter in remaining whose prereqs are all in covered
    for v in sorted(remaining):
        if all(p in covered for p in prereqs[v]):
            schedule.append(v)
            covered.add(v)
            remaining.remove(v)
            break

# 4) print with names
titles = {
    2:  "Fundamental Algorithms",
    3:  "The Euclidean Algorithm",
    4:  "Applications of Euclid's Algorithm",
    5:  "Modular Algorithms",
    6:  "Resultants and GCD Computation",
    8:  "Fast Multiplication",
    9:  "Newton Iteration",
    10: "Fast Evaluation and Interpolation",
    11: "Fast Euclidean Algorithm",
    12: "Fast Linear Algebra",
    14: "Factoring over Finite Fields",
}

print("Your course sequence is:")
for ch in schedule:
    print(f"  Chapter {ch}: {titles[ch]}")